|Weird...this one has me scratching my head too...|
I think the VARIALHOSTING host is misconfigured, it doens't list itself as the SOA (source of authority):
# dig @NS1.VARIALHOSTING.COM sanlucardebarramedagolf.com
; QUESTION SECTION:
;sanlucardebarramedagolf.com. IN A
;; ANSWER SECTION:
sanlucardebarramedagolf.com. 14400 IN A 18.104.22.168
;; AUTHORITY SECTION:
sanlucardebarramedagolf.com. 86400 IN NS ns4.awardspace.com.
sanlucardebarramedagolf.com. 86400 IN NS ns1.awardspace.com.
sanlucardebarramedagolf.com. 86400 IN NS ns2.awardspace.com.
sanlucardebarramedagolf.com. 86400 IN NS ns3.awardspace.com.
So...NS1.VARIALHOSTING.COM returns an Address record, then says the Authorative is awardspace.com, which has the old address...
-You clear DNS cache
-NS1.VARIALHOSTING.COM returns correct A, A and SOA are cached locally
-4 hours later, cache expires, A removed
-Client now re-requets A from the cached SOA (which is awardspace)
-Awardspace returns the old address
-SOA is cached as Awardspace, so old address will continue to be returned until the SOA cache is removed & then we start over again...
...weird though. If NS1.VARIALHOSTING.COM isn't the SOA, it shouldn't return an address record (because it's not the authority, or at least doesn't think it is...)
I'd double check the DNS setup on VARIALHOSTING.com & verify you've transfered the zone/soa to VARIALHOSTING.COM & it's the master server.
Also, delete the A / SOA records from the old host (awardspace.com)